Using a nonparametric test when we could employ a parametric test can be less efficient because a nonparametric test often tends to ignore available sample information; for example, by focusing only on the directions rather than the sizes of observed differences.

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Nonparametric tests do not rely on assumptions about the underlying distribution of the data, but they may be less powerful than parametric tests in detecting differences or associations between variables, especially when sample sizes are large and data are normally distributed. Nonparametric tests may also require larger sample sizes to achieve the same level of significance as parametric tests, and they may be less informative in terms of estimating effect sizes or confidence intervals. However, nonparametric tests are often more robust to outliers or non-normality, and they may be preferred when the assumptions of parametric tests are violated or when the data are ordinal or categorical rather than continuous. Ultimately, the choice between parametric and nonparametric tests should depend on the research question, the type and distribution of the data, the sample size, and the level of statistical power and precision required.

Using a Nonparametric Test When We Could Employ a Parametric